Transcript Chapter 04 ppt - Ivy Tech -

GEOMETRIC
CONSTRUCTION
CHAPTERFOUR
OBJECTIVES
1. Identify the geometry that makes up basic 2D drawings.
2. Use board drafting or 2D CAD skills to create technical
figures.
3. Describe the advantages of CAD contrasted with
drawing with manual instruments
Technical Drawing with Engineering Graphics, 14/e
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GEOMETRY REVIEW
• Triangles
• Quadrilaterals
• Polygons
• Circles
• Arcs
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Giesecke, Hill, Spencer, Dygdon, Novak, Lockhart, Goodman
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BISECTING A LINE OR
CIRCULAR ARC
Compass system
Triangle and T-Square System
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BISECTING A LINE WITH TRIANGLE
AND T-SQUARE
From endpoints A and B, draw construction lines at 30°, 45°, or 60° with the given line.
Then, through their intersection, C, draw a line perpendicular to the given line to locate
the center D…
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Triangles
Inclined lines can be drawn at standard angles with the 45° triangle and the
30° x 60° triangle. The triangles are transparent so that you can see the lines
of the drawing through them. A useful combination of triangles is the 30° x 60°
triangle with a long side of 10" and a 45° triangle with each side 8" long.
Technical Drawing with Engineering Graphics, 14/e
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Any Angle in 15° Increments
With only a 30° x 60°
triangle and a 45°
triangle, you can draw
any angle in 15°
increments
The bottom
of the triangle in
each case is resting
on the blade of the
T-square. Twenty-four 15°
sectors are possible with just
these two triangles used
singly or in combination.
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Protractors
For measuring or setting off angles other than those obtainable with
triangles, use a protractor.
Plastic protractors are
satisfactory for most
angular measurements
Nickel silver protractors are
available when high accuracy
is required
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ANGLES…
BISECTING AN ANGLE
TRANSFERRING AN
ANGLE
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Upper Saddle River, NJ 07458. • All Rights Reserved.
DRAWING A LINE PARALLEL TO A
LINE AND AT A GIVEN DISTANCE
T-square Method
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For Curves
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DRAWING A LINE THROUGH A POINT
AND PERPENDICULAR TO A LINE
When the Point Is Not on the Line
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When the Point Is on the Line
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T-square Method
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TRIANGLES…
DRAWING A TRIANGLE
WITH SIDES GIVEN
DRAWING A RIGHT
TRIANGLE WITH
HYPOTENUSE AND ONE
SIDE GIVEN
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LAYING OUT AN ANGLE
• Tangent Method
• Sine Method
• Chord Method
Many angles can be laid out directly with the triangle or protractor.
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© 2012, 2009, 2003, Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved.
DRAWING AN EQUILATERAL
TRIANGLE
Alternative Method
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Upper Saddle River, NJ 07458. • All Rights Reserved.
DRAWING A SQUARE
• T-square Method
• Diameters Method
• Inscribed Circle Method
You can use the AutoCAD Polygon
command to draw squares. The
Rectangle command is another quick
way to make a square in AutoCAD.
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DRAWING A REGULAR PENTAGON
Dividers Method
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Geometric Method
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DRAWING A HEXAGON
Each side of a hexagon is equal to the radius of the circumscribed circle
Use a compass
Centerline Variation
Steps
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Drawing an Octagon
Given an inscribed circle, or distance
“across flats”, use a T-square or
straightedge and a 45° triangle to draw
the eight sides tangent to the circle.
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Given a circumscribed square, (the distance
“across flats”) draw the diagonals of the
square. Then, use the corners of the square
as centers and half the diagonal as the
radius to draw arcs cutting the sides
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FINDING THE CENTER OF A CIRCLE
This method uses the principle that any right triangle inscribed in a circle
cuts off a semicircle.
Another method, slightly longer, is to reverse the procedure. Draw two
nonparallel chords and draw perpendicular bisectors. The intersection of the
bisectors will be the center of the circle.
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DRAWING TANGENTS TO TWO
CIRCLES
AutoCAD software provides a
convenient object snap for
finding tangency.
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DRAWING AN ARC TANGENT TO A
LINE OR ARC
AND THROUGH A POINT
Tangents
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DRAWING AN ARC TANGENT TO TWO
LINES AT RIGHT ANGLES
For small radii, such as 1/8R for fillets and rounds, it is not practicable
to draw complete tangency constructions. Instead, draw a 45° bisector
of the angle and locate the center of the arc by trial along this line
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DRAWING AN ARC TANGENT TO TWO
LINES AT ACUTE OR
OBTUSE ANGLES
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Upper Saddle River, NJ 07458. • All Rights Reserved.
DRAWING AN ARC TANGENT TO AN
ARC AND A STRAIGHT LINE
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Upper Saddle River, NJ 07458. • All Rights Reserved.
DRAWING AN ARC TANGENT TO TWO
ARCS
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Drawing an Arc Tangent to Two Arcs and
Enclosing One or Both
Technical Drawing with Engineering Graphics, 14/e
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DRAWING AN OGEE CURVE
Connecting Two Parallel Lines
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Connecting Two Nonparallel Lines
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THE CONIC SECTIONS
The conic sections are curves produced by planes intersecting a right circular
cone.
Four types of curves are produced: the circle, ellipse, parabola, and
hyperbola, according to the position of the planes.
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DRAWING A FOCI ELLIPSE
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DRAWING A CONCENTRIC CIRCLE
ELLIPSE
If a circle is viewed with the line of sight perpendicular to the plane
of the circle…
…the circle will appear as a circle, in true size and shape
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DRAWING A PARALLELOGRAM
ELLIPSE
The intersection of like-numbered lines will be points on the ellipse. Locate points in the
remaining three quadrants in a similar manner. Sketch the ellipse lightly through the points,
then darken the final ellipse with the aid of an irregular curve.
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ELLIPSE TEMPLATES
These ellipse guides are usually designated by the ellipse angle, the
angle at which a circle is viewed to appear as an ellipse.
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Irregular Curves
The curves are largely successive segments of geometric curves,
such as the ellipse, parabola, hyperbola, and involute.
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© 2012, 2009, 2003, Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved.
DRAWING AN APPROXIMATE ELLIPSE
For many purposes, particularly where a small ellipse is required, use the
approximate circular arc method.
Technical Drawing with Engineering Graphics, 14/e
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© 2012, 2009, 2003, Pearson Higher Education,
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DRAWING A PARABOLA
The curve of intersection between a right circular cone and a plane parallel
to one of its elements is a parabola.
Technical Drawing with Engineering Graphics, 14/e
Giesecke, Hill, Spencer, Dygdon, Novak, Lockhart, Goodman
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© 2012, 2009, 2003, Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved.
DRAWING A HELIX
A helix is generated by a point moving around and along the surface of a
cylinder or cone with a uniform angular velocity about the axis, and with a
uniform linear velocity about the axis, and with a uniform velocity in the
direction of the axis
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DRAWING AN INVOLUTE
An involute is the path of a point on a string as the string unwinds from a line,
polygon, or circle.
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Upper Saddle River, NJ 07458. • All Rights Reserved.
DRAWING A CYCLOID
A cycloid is generated by a point P on the circumference of a circle that
rolls along a straight line
Cycloid
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DRAWING AN EPICYCLOID OR A
HYPOCYCLOID
Like cycloids, these curves are used to form the outlines of certain gear teeth and are therefore
of practical importance in machine design.
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© 2012, 2009, 2003, Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved.